Bogdan's opportunities will be limited at Anfield next season.
Bogdan fell out of favour last season under manager Jurgen Klopp and was eventually demoted to third choice when Danny Ward was recalled from his loan spell at Aberdeen after making his fair share of errors during his six appearances for the Reds.
Ward himself is expected to head out on loan to Huddersfield Town after extending his contract, the report states, while Bogdan finds himself behind new signing Loris Karius and last season's number one Simon Mignolet in the goalkeeping pecking order.
The Hungary international is said to be desperate for first-team football next season and would like to go out on loan.
He is quoted, saying: “The goal is to get loaned out. I could stay but I would need incredible luck or a lot of injuries to climb the ladder.
“I can get out of this situation by performing well somewhere else. Then if life allows it, return to Liverpool. I need to go to prove my worth.”
Bodgan has made it clear of his desire for first-team football, and he does not look as if he will get it at Liverpool any time soon, especially if he could not break into the side despite some questionable goalkeeping from Mignolet at different stages during the season.
A loan move could be the best for all parties with Karius and Mignolet competing for the number one spot, but Liverpool may want the option to recall Bogdan if anything happens to either of their other two goalkeeping options purely as cover, although Ryan Fulton is another option the Reds have should he be needed.